As for Mayor Wilkins, he said that he was the founder of Sunnydale, that he had no soul, and that he was immortal (which would tie in well with the "founder of Sunnydale" statement. But in order to actually become a demon, he had to eat those bug things. Probably, at some point several hundred years earlier, he made one of those deals with someone or some THING that would make him immortal in exchange for his soul. Most likely, he wasn't a permanent resident of Sunnydale for all of those years, but rather stayed there for awhile, then moved away for a few years, then returned as his own son, nephew, or something, then repeated the process whenever necessary, sort of like Robert Heinlein's character, Lazarus Long, did. In that way, he could keep tabs on the hellmouth while traveling all over the world studying and gathering all of the information that he would eventually need to trigger his Ascension. Then, when the time was right, he moved back "home," set up his identity, worked his way into being elected mayor, and set up his final plans. Just his luck, some airhead Slayer moved in with a big lumbering Neanderthal vampire following her around like a love sick puppy, complicating all of his best laid schemes.
As for becoming a demon, I think that they were distinct species who reproduced in a more or less normal way. Werewolves are the result of the equivalent of a supernatural disease, passed on by biting, and vampires are demon possessed and reanimated corpses, neither one actual demons, more "halfbreeds" as Ilyria described them. So you can't actually become a demon. Sorry to disappoint you if you had your heart set on it...